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Topic One way ANOVA, Non normal data

One way ANOVA, Non normal data

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This topic contains 10 replies, has 6 voices, and was last updated by Profile photo of Deep Deep 11 years, 9 months ago.

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    I have data of six different hieght. It is actually the hieght of a small projection that we make when we stamp the part. We use the same tool(i mean the same height tool) for each projection. I wanted to check the hieght of all the six projections are same or not. I got sample size as 12, but i took 20 samples because its easy to measure and the part is not costly. I am treating the seven height (1,2,3,4,5,6,)as six levels and doing a one way ANOVA. The problem is some of these hieght data are normal and some are not. I think all these datas(1,2,3,4,5,6) should be normal to do ANOVA. What can i do here? Any suggestions.? If data is needed to give suggestions please check here.  ftp://nick:password@
    Thanks in advance


    Sample size is small.  If data sets are not normal you can always try a Medians test in lieu of a Means test.


    If faced with a non-normal distribution, you have several options: 

    Transform the data..generally not considered the best option
    Increase your sample size and use the CLT to chase normality
    Use a nonparametic test.  Here is an excerpt from MTB. You might find it helpful.  In MTB use:  STAT>Nonparametrics>Moods Median, etc.  Good luck.

    Mood’s median test can be used to test the equality of medians from two or more populations and, like the Kruskal-Wallis Test, provides an nonparametric alternative to the one-way analysis of variance. Mood’s median test is sometimes called a median test or sign scores test. Mood’s median test tests:
    H0: the population medians are all equal versus H1: the medians are not all equal
    An assumption of Mood’s median test is that the data from each population are independent random samples and the population distributions have the same shape. Mood’s median test is robust against outliers and errors in data and is particularly appropriate in the preliminary stages of analysis. Mood’s median test is more robust than is the Kruskal-Wallis test against outliers, but is less powerful for data from many distributions, including the normal.


    What in the world do you mean by this?
    Increase your sample size and use the CLT to chase normality
    It makes no sense.


    Perhaps I mis-spoke…..
    The central limit theorem states that given a distribution with a mean m and variance s2, the sampling distribution of the mean appraches a normal distribution with a mean and variance/N as N, the sample size, increases
    It was my understanding the CLT (central limit theorm) indicates a data set will move toward normality as you increase its size….please correct me if this is inaccurate.


    First paragraph is correct, second is not.  The CLT does not state that increasing the size of the data causes the distribution to move toward a normal one.  The distribution of the population is what it is.
    As you pull samples from this population distribution and then measure the means of the samples, the distribution of the sample means will tend more toward normality as your sample size increases…but, that is what you said, basically, in the first paragraph.


    I did indeed miss-speak.  Thank you for correcting me.


    How are you testing for normality?   With a sample size of 12 – a histogram will not show a normal curve.  I would use a probability plot.  This may help.   If you can I would collect more data –Increasing the number of samples will give you more information (measurements) to prove or disprove whether or not you have a normal distribution. 


    Thanks a lot for all the comments;
    kkh: I did check normality using normal curve. Got the same results, some are normal some are not.
    Everyone here thinks that its the low sample size. I calculated the sample size like this..
    Tolerance is 1.8 +/-.25, but the data are in inches, tolerance in inches is 0.061 – 0.081
    Number of levels = 6. max difference = .01      standard deviation = .01
    I got 34 for .9 power value. But when i did before i got sample size as 12 (thats why i took 20 readings), but i cannot remember the std deviation that i used. The std deviation above is from the data i have now (the 20 set data). Anyway thanks for the comments.  I wil take more samples. But will that make any difference to the normality?
    Thanks once again.


    You said  “I will take more samples. But will that make any difference to the normality?” 
    As Obiwan said earlier “The CLT does not state that increasing the size of the data causes the distribution to move toward a normal one.  The distribution of the population is what it is.”  
     IF —-your first (smaller) sample was truely a representation of the process – then your results will be the same (or very close).  However,  if the sample size did not represent the process or you did not collect the data correctly then yes you will see a difference in the results -BUT it does not change the normality – it was always what it was– you will not see the true results if you do not take a sample that represents the population (process) from which it came!!!!!  Does this make sense? 
    Good Luck….. 
    Doing a Oneway ANOVA is a comparison test…  I am usually more concerned with equal variances than normality….To me that is the important question/assumption to prove.


    Thanks a lot. That does make some sense. I have one more question. In my previous post i did mention about the way i calculate the sample size. Is that correct? Just double checking
    thanks once again

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